Thanks, the Jisho link is useful. The sentence makes a lot more sense with ‘to relax’ as a translation.
I won’t try and explain my rather muddled attempt at understanding およげるようになるには…
Page 65:
でも、およげない 人でも、かんたんに 水に うく ことが できる みずうみが あるのを 知っています。
However, did you know there is a lake where even people that can not swim can float easily (in the water)? Lose translation
アシアの 西、ヨルダンと パレスチナ、イスラエルに またがる 場所に 死海と いう みずうみが あります。
In West Asia, Jordan and Palestine, in a place that extends over Israel, there is a lake called “Death Sea”
死海とは、ちょっと こわい 名前ですが、いったい どんな みずうみなんでしょう。
The Death Sea has a name a little scary, but what the heck is this lake?
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Page 65, hope you are all having a good Christmas. 
でも、およげない 人でも、かんたんに 水に うく ことが できる みずうみが あるのを 知っていますか。
But, did you know that there is a lake where even people who cannot swim are able to float easily in the water?
アジアの 西、ヨルダンと パレスチナ、イスラエルに またがる 場所に 死海と いう みずうみが あります。
There is a a lake called the Dead Sea in the west of Asia, in a place spanning Jordan, Palestine and Israel.
死海とは、ちょっと こわい 名前ですが、いったい どんな みずうみなんでしょう。
What on earth kind of lake is the Dead Sea - the name is a bit scary.
大むかしは、この あたりは 海でした。
Long ago, this bank was the sea.
気おんが 高く, 水分が じょうはつしていき、海と 切りはなされて みずうみに なりました。
Atmospheric temperature rose, water evaporated and the sea bounds built up and became the lake.
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I think your translation “in order to be able to swim” looks OK.
およげる = can swim (potential of およぐ)
ようになる = to reach the point that
には = in order to
Literally: In order to reach the point that one can swim
Loosely : In order to be able to swim
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P64
およげるように なるには、まず 体の 力を ぬいて、 うまく 水に うく ことが コツですね。
In order to be able to swim, first relax your body, as floating well in the water is the key, right?
To me, although the clause まず 体の 力を ぬいて has a verb in て- form it doesn’t look like a conjunction meaning “and”. This clause might be a participial phrase or what DOJG calls a “participial construction”.
Here’s one of their example sentences–
わたしは コートを脱いで ハンガーにかけた。
Taking off my coat, I hung it on a hanger.
Second possible translation–
In order to be able to swim, the key is to float well in the water which starts with relaxing your body, right?
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I think でしょう in this context can be translated as “I wonder” rather than “probably” or something else.
Here’s an example sentence from here.
それは何でしょう。I wonder what that is.
Dead Sea is a name that’s a little scary but I wonder what in the world kind of lake it is.
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Page 65:
Not sure… the “book” knows that it is, and is asking if you know it.
My guest is that is asking you what it is, but with a certain degree of uncertainty…
bla bla bla. … but what heck is this lake???
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Yes, I think you are right in that it does convey uncertainty but exactly how the uncertainty gets translated into English is kind of fuzzy sometimes.
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Page 66;
今では、海の 水面の 高さより、およそ 四百メートルも ひくい 場所に あります。
Nowadays, from the height of the sea water surface there is approximately even 400 meters in the lowest place Not sure about the end
これだけ 水分が じょうはつし、土の 中の しおも とけでてきたため、 海水の 十倍もの しおを ふくんでいるのです。
So much water evaporated, even the salt in the dirt has been dissolved as a consequence, that the sea water contains ten times the regular amount of salt Lose translation, and again doubting with the も
このため、 ほとんどの せいぶつは 生きる ことが できません。
Because of this, there isn’t almost any living thing (living things are not able to live)
それで、 「死海」と よばれているのです。
And that’s why it’s called the “Dead Sea”
海で およぐと、 プールよりも 少し うきやすいと かんじませんか。
When you swim in the sea, does it feels a little bit easier in compassion to the pool?
Bu the way, I think it’s the first page with Kanjis without furigana, although they are only numbers
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I think I have seen this on some previous pages. I think all number kanji do not have furigana for 一 through to 十. Things like 百 seem to be exceptions.
I will have a bunch of free time tomorrow so I will update the docs with the page start sentences and end sentences with as many pages as I can. 
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Page 63
Just finishing off the last of the mince pies, switching vacation mode off, and getting back to the book! (I adore Christmas, but any Japanese I once knew has now drained away completely from my brain!)
Anyway, can anyone shed some light on this 行われる?
Jisho has it down as “to be done”, but how does that fit in with ロシアで 行われる 百夜祭?
Thanks for any help anyone can offer!
Page 64
In order to swim, the trick is to relax your body and to completely float in the water.
Does this look like an okay-ish translation at all?
Welcome back!
The other meanings in the Jisho link include - “to take place” and “to be held.” In Russia, is held, a midnight sun festival.
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Thank you! And, ah ha! I see! (Sorry! I ought to have spotted that right away! Your translation is perfect, I just couldn’t see why! Now I do! Thank you!)
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Page 66
今では、海の 水面の 高さより、およそ 四百メートルも ひくい 場所に あります
今では、nowadays
海の - the sea’s
水面の 高さ - water level
より、 - more than
およそ -about
四百メートルも - 400 meters
ひくい - low
場所に - place + に
あります - there is
Nowadays there are places where the sea’s water level is about 400 meters lower [than that of the sea it used to belong to].
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I can see it
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Thank you!
Added images for up to page 80-81 in the Google docs earlier, hope this helps. I’ll try and complete the rest of this chapter tomorrow.
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Page 67
プールの 水と, 海の しお水とでは, しお水の ほうが ものを うかせる 力 (浮力と いいます) が より 強く なります。
I have no idea! (but quickly getting my ideas down before emucat provides the translation! lol!)
プールの水と, - pool’s water + と (if, when)
海のしお水 - sea’s salt water
とでは, - between (?? not sure how this works!)
しお水の - salt water’s
ほうが - I always have trouble with comparisons!
ものを - things’s
うかせる - 浮かせる - to float
力 - power
(浮力と いいます) が - called floating power = buoyancy + が
より - than
強くなります - becomes strong
Something about the salt water in the [Dead] sea providing more buoyancy than that of water in swimming pools.
Edit: second attempt:
Between the water in a swimming pool and salt water in the sea, salt water has stronger buoyancy.
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Don’t worry, I’m trying to crack the “Descend to B3 password”
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